Dynamic Multi-objective Optimization Research Articles

Dynamic multi-objective optimization based on classification response of decision variables

In recent years, many dynamic multi-objective optimization algorithms (DMOAs) have been proposed to address dynamic multi-objective optimization problems (DMOPs). Most existing DMOAs treat all decision variables uniformly and respond to them in an identical manner. This paper proposes a dynamic multi-objective optimization algorithm based on the classification response of decision variables (CRDV-DMO). Firstly, CRDV-DMO categorizes the decision variables into convergence variables and diversity variables. Different decision variables adopt distinct response strategies. The response strategy of diversity variable (RSDV) uses Latin hypercube sampling to generate the diversity variables of the new environment. For each dimensional convergence variable, the response strategy of convergence variable (RSCV) first evaluates whether the basic center prediction strategy (CPS) yields positive feedback or negative feedback, further determining the predictability of that dimensional convergence variable. RSCV then decides to either use the basic CPS to generate the convergence variable for that dimension or to retain that dimensional convergence variable from the current environment, based on the predictability of that dimensional convergence variable. The proposed algorithm is extensively studied through comparison with several advanced DMOAs, demonstrating its effectiveness in dealing with the benchmark DMOPs and the parameter-tuning problem of the PID controller on a dynamic system.

Dynamic Multiobjective Optimization Based on Multi-Environment Knowledge Selection and Transfer

Background: Dynamic multiobjective optimization problems (DMOPs) involve multiple conflicting and time-varying objectives, and dynamic multiobjective algorithms (DMOAs) aim to find Pareto optima that are closer to the real one in the new environment as soon as possible. In particular, the introduction of transfer learning in DMOAs has led to good results in solving DMOPs. However, the selection of valuable historical knowledge and the mitigation of negative transfer remain important problems in existing transfer learning-based DMOAs. Method: A DMOA based on multi-environment knowledge selection and transfer (MST-DMOA) is proposed in this article. First, by clustering historical Pareto optima, some representative solutions that can reflect the main evolutionary information are selected as knowledge of the environment. Second, the similarity between the historical and current environments is evaluated, and then the knowledge of multiple similar environments is selected as valuable historical knowledge to construct the source domain. Third, solutions with high quality in the new environment are obtained to form the target domain, which can better help historical knowledge to adapt to the current environment, thus effectively alleviating negative transfer. Conclusions: We compare the proposed MST-DMOA with five state-of-the-art DMOAs on fourteen benchmark test problems, and the experimental results verify the excellent performance of MST-DMOA in solving DMOPs.

A dynamic multi-objective optimization evolutionary algorithm based on classification of environmental change intensity and collaborative prediction strategy

A dynamic multi-objective optimization evolutionary algorithm based on classification of environmental change intensity and collaborative prediction strategy

Integrating machine learning with dynamic multi-objective optimization for real-time decision-making

Real-time decision-making in dynamic multi-objective optimization problems (DMOPs) is challenging due to constantly changing objectives and constraints. This paper integrates machine learning with Non-dominated Sorting Genetic Algorithm II (NSGA-II) to solve DMOPs and make real-time decisions. Learning-based methods have gained popularity for predicting solutions in new environments and capturing changing patterns in optimal solutions. However, existing approaches often struggle with training difficulty and reduced prediction accuracy due to irrelevant or redundant variables. Therefore, we introduce a new interdependent prediction (IDP) technique to identify correlations between variables and prediction targets and select significant variables for a predictive model. In this way, a better initial population is predicted. The IDP strategy is integrated within the dynamic NSGA-II, introducing a new algorithm called IDP-DNSGA-II. This integration facilitates rapid convergence, finding optimal or near-optimal solutions. The proposed method is evaluated against standard benchmarks, demonstrating superior performance in convergence speed and solution diversity with the changes in the problem environment. The IDP-DNSGA-II is validated through real-world optimization challenges in sustainable automobile production distribution in order-to-delivery systems to enhance environmental sustainability and operational efficiency. This study identifies the minimum frequency of change required in real-world problems to adequately track the optimal decision in real-time.

A dynamic multi-objective optimization model for inner-industry carbon responsibility allocation based on carbon tax and carbon offsets accounting

The setting of Intergovernmental Panel on Climate Change (IPCC) raises concerns on curbing the excessive carbon emissions, and European Union (EU) has been proactively attempting “green” initiatives striving to achieve carbon neutrality. The current Carbon Border Adjustment Mechanism (CBAM) only works on short-term carbon reduction without much “greenness” investment incentives so far, and few studies focus on the long-standing inner-industrial carbon reduction coordination. To address these issues, this paper creatively presents a dynamic multi-objective carbon responsibility allocation model (CRAM) for EU carbon market, allows the carbon trade with a taxation based on carbon offsets accounting, and considers the final targets of sustainable “greenness” investment incentives. To find the optimal results of the designed dynamic CRAM, an improved KT-NSGA-II algorithm is proposed to detect the Pareto frontiers of each successive periods. Data from EU Cement and Aluminium industries are then selected for empirical analysis to compare the proposed CRAM to conventional CBAM model. The findings demonstrate that the superiority of CRAM in carbon emissions reduction, economic benefits improvement and green invests encouragement. With the adjustment of the inner-industrial carbon allowance trade, total carbon emissions decreased by 28.03% and the “greenness” investment initiative increased by 39.24% in contrast to the CBAM. The sensitivity analysis of the model also provides suggestions on the settings of carbon quota and tax with different industrial production process, and proposes policy recommendations for CRAM implementation.

Strategic decision-making for sustainable production and distribution in automotive industry: a machine learning enabled dynamic multi-objective optimisation

ABSTRACT Over the last decade, numerous researchers have disclosed that major automotive companies do not conform to regulatory or societal expectations regarding their environmental and social performances. This paper explores the dynamic capabilities of production distribution within the sustainability practices of automotive industries. It offers insights to better grasp and articulate the environmental, economic, and social dimensions of sustainable supply chains. The research framework encloses all supply chain phases, from raw material sourcing to retailing finished products. Three conflicting objective functions are identified: social advantages maximisation, cost minimisation, and emission minimisation. Specifically, the study tackles a dynamic multi-objective optimisation model where each automobile type faces a series of dynamic demands. The dynamic nature of the problem poses significant challenges to conventional evolutionary algorithms for detecting the optimal solutions over time. Therefore, we introduce an interconnected prediction-based dynamic non-dominated sorting algorithm (ICP-DNSGA-II). Finally, extensive computational experiments are conducted to assess the effectiveness of this holistic approach. The findings offer valuable insights for automotive industry stakeholders and policymakers, illustrating its potential to enhance operational efficiency and sustainability performance across the supply chain. Most importantly, this paper proposes an automated decision-making approach to generate optimal solutions with dynamic changes in market demands.

Knowledge hierarchy-based dynamic multi-objective optimization method for AUV path planning in cooperative search missions

This study focuses on path planning for Autonomous Underwater Vehicles (AUVs) in underwater cooperative search missions. The complexities of the ocean environment, the uncertainty of target movements, and limited communication capabilities render underwater cooperative search missions dynamic multi-objective optimization challenges. Studies focusing on communication-constrained search strategies still lack reliable metrics for assessing underwater communication quality and do not consider communication dead zones. Addressing these deficiencies, this paper introduces a novel communication optimization strategy utilizing packet error rate as a metric for assessing communication efficacy, complemented by a potential field-based method for navigating out of communication dead zones. To tackle the inherently dynamic nature of cooperative search missions for mobile underwater targets, we propose a dynamic multi-objective optimization algorithm that employs a knowledge hierarchy strategy. This method enhances the NSGA-II algorithm's efficiency by extracting effective gene segments from historical Pareto solution set and generating a new initial population through recombination, hierarchy, and prediction. Distinct from other advanced dynamic multi-objective optimization approaches that are limited to theoretical problems, our approach is directly applicable to practical scenarios. The effectiveness and practicality of the proposed method are validated through a series of simulation experiments considering the impact of underwater acoustic communication. These results demonstrate that this research is not only innovative in theory but also holds significant engineering value and practical prospects in real-world applications.

Learning to Guide Particle Search for Dynamic Multiobjective Optimization.

Dynamic multiobjective optimization problems (DMOPs) are characterized by multiple objectives that change over time in varying environments. More specifically, environmental changes can be described as various dynamics. However, it is difficult for existing dynamic multiobjective algorithms (DMOAs) to handle DMOPs due to their inability to learn in different environments to guide the search. Besides, solving DMOPs is typically an online task, requiring low computational cost of a DMOA. To address the above challenges, we propose a particle search guidance network (PSGN), capable of directing individuals' search actions, including learning target selection and acceleration coefficient control. PSGN can learn the actions that should be taken in each environment through rewarding or punishing the network by reinforcement learning. Thus, PSGN is capable of tackling DMOPs of various dynamics. Additionally, we efficiently adjust PSGN hidden nodes and update the output weights in an incremental learning way, enabling PSGN to direct particle search at a low computational cost. We compare the proposed PSGN with seven state-of-the-art algorithms, and the excellent performance of PSGN verifies that it can handle DMOPs of various dynamics in a computationally very efficient way.

The IGD-based prediction strategy for dynamic multi-objective optimization

In recent years, an increasing number of prediction-based strategies have shown promising results in handling dynamic multi-objective optimization problems (DMOPs), and prediction models are also considered to be very favorable. Nevertheless, some linear prediction models may not always be effective. In particular, when the motion direction trends of different individuals are not aligned, these models can yield inaccurate prediction results. Inverted generational distance (IGD) is a commonly used metric for evaluating the performance of algorithms. This paper proposes a prediction model based on the IGD metric. Specifically, we assume that the pareto optimal front (POF) of the population at the previous time step is the true POF, and the POF at the current time step is the approximate POF. We cluster the current population with reference to the euclidean distances from uniform points on the true POF to the current POF points, with slight overlap between adjacent clusters, enables a better tradeoff between convergence and diversity in the prediction process. We consider the movement directions of individuals within each cluster separately through different cluster distributions, while balancing the individual movement directions and the overall population movement direction by overlaying cluster coverage areas, thereby helping to avoid the clustered prediction population from getting trapped in local optima. Experimental results and comparisons with other algorithms demonstrate that this strategy exhibits strong competitiveness in handling DMOPs.

A Novel Multi-Objective Dynamic Reliability Optimization Approach for a Planetary Gear Transmission Mechanism

Planetary gear transmission mechanisms (PGTMs) are widely used in mechanical transmission systems due to their compact structure and high transmission efficiency. To implement the reliability design and optimization of a PGTM, a novel multi-objective dynamic reliability optimization approach is proposed. First, a multi-objective reliability optimization model is established. Furthermore, considering the strength degradation of gears during service, a dynamic reliability analysis is conducted based on the theory of nonlinear fatigue damage accumulation. In addition, to improve computing efficiency, a random forest surrogate model based on the particle swarm optimization algorithm is proposed. Finally, an adaptive multi-objective evolutionary algorithm based on decomposition (AMOEA/D) is designed to optimize the mechanism, along with an adaptive neighborhood updating strategy and a hybrid crossover operator. The feasibility and superiority of the proposed approach are verified through an NGW planetary gear reducer. The results show that the proposed surrogate model can reduce the calculation cost and has high accuracy. The AMOEA/D algorithm can improve transmission efficiency, reduce gear volume and ensure reliability at the same time. It can provide guidance for actual gear production.

A Framework Based on Historical Evolution Learning for Dynamic Multiobjective Optimization

A Framework Based on Historical Evolution Learning for Dynamic Multiobjective Optimization

Fusion prediction strategy-based dynamic multi-objective sparrow search algorithm

Solving dynamic multi-objective optimization problems with time-varying Pareto front (PF) or Pareto set (PS) is a challenging task. Such problems require algorithms to react to environmental changes and efficiently track optimal solutions. For this purpose, a dynamic multi-objective sparrow search algorithm (SSA) with fusion prediction strategy, based on difference model and kernel extreme learning machine (DMOSSA-FPS), is proposed. Given the diversity of change characteristics, a single prediction model is insufficient. Therefore, based on the historical information of the population, a difference model and a kernel extreme learning machine are integrated for PS prediction. The former is used to predict the solutions of some individuals under approximate linear changes and the latter is employed for nonlinear predictions. In a new environment, the combined predictions increase the diversity of the initial population. Additionally, a new static optimizer is proposed, which combines decomposition- and dominance-based approaches to constitute a new individual screening mechanism. Then the optimization mode of SSA is introduced to enhance both algorithmic diversity and convergence rate. The experimental results on the DF test suite demonstrate that, compared with several other advanced algorithms, DMOSSA-FPS exhibits stronger convergence and robustness.

A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategy

Dynamic multiobjective optimization problems (DMOPs) typically involve multiple conflicting time-varying objectives that require optimization algorithms to quickly track the changing Pareto-optimal front (POF). To this end, several methods have been developed to predict new locations of moving Pareto-optimal solution set (POS) so that populations can be re-initialized around the predicted locations. In this paper, a dynamic multi-objective optimization algorithm based on a multi-directional difference model (MOEA/D-MDDM) is proposed. The multi-directional difference model predicts the initial population through the estimated populations developed by a designed POS estimation strategy. An adaptive crossover-rate approach is incorporated into the optimization process to cope with different POS structures. To investigate the performance of the proposed approach, MOEA/D-MDDM has been compared with six state-of-the-art dynamic multiobjective optimization evolutionary algorithms (DMOEAs) on 19 benchmark problems. The experimental results demonstrate that the proposed algorithm can effectively deal with DMOPs whose POS has a single-modality characteristic and continuous manifolds.

Hybrid response dynamic multi-objective optimization algorithm based on multi-arm bandit model

Dynamic multi-objective optimization is a relatively challenging problem within the field of multi-objective optimization. Nevertheless, these problems have significant real-world applications. The key to addressing dynamic multi-objective problems effectively is promptly tracking changes in the Pareto set (PS) and Pareto front (PF). Dynamic multi-objective optimization encompasses various types of problems, and a single-type response strategy proves effective for some specific scenarios. However, as problem complexity and diversity increase, a single-type response strategy often falls short in solving dynamic multi-objective optimization problems. To address this issue, this paper proposes a hybrid response dynamic multi-objective optimization algorithm. The suggested algorithm utilizes the multi-arm bandit model to adaptively adjust the proportion of different response strategies for each type of multi-objective optimization problem. Furthermore, it achieves rapid convergence through an enhanced two-stage MOEA/D. Experiments demonstrate the effectiveness of the strategies employed in the proposed algorithm and its competitiveness compared to other state-of-the-art algorithms.

A dynamic multi-objective evolutionary algorithm with variable stepsize and dual prediction strategies

The prediction strategy is a key method for solving dynamic multi-objective optimization problems (DMOPs), particularly the commonly used linear prediction strategy, which has an advantage in solving problems with regular changes. However, using the linear prediction strategy may have limited advantages in addressing problems with complex changes, as it may result in the loss of population diversity. To tackle this issue, this paper proposes a dynamic multi-objective optimization algorithm with variable stepsize and dual prediction strategies (VSDPS), which aims to maintain population diversity while making predictions. When an environmental change is detected, the variable stepsize is first calculated. The stepsize of the nondominated solutions is expressed by the centroid of the population, while the stepsize of the dominated solutions is determined by the centroids of the clustered subpopulations. Then, the dual prediction strategies combine an improved linear prediction strategy with a dynamic particle swarm prediction strategy to track the new Pareto-optimal front (PF) or Pareto-optimal set (PS). The improved linear prediction strategy aims to enhance the convergence of the population, while the dynamic particle swarm prediction strategy focuses on preserving the diversity of the population. There have also been some improvements made in the static optimization phase, which are advantageous for both population convergence and diversity. VSDPS is compared with six state-of-the-art dynamic multi-objective evolutionary algorithms (DMOEAs) on 28 test instances. The experimental results demonstrate that VSDPS outperforms the compared algorithms in most instances.

An online cooperative control strategy for enhancing microgrid participation into electricity market

This paper develops a cooperative control methodology for the online energy management of grid-connected microgrids. The main aim of this methodology is to actively manage the active power outputs of all dispatchable energy sources available within the microgrid as well as the power exchanged with the utility grid so as to match the total load demand at the minimum operating cost. This implies to solve a constrained multi-objective dynamic optimization problem aimed at minimizing the total microgrid operating costs and ensuring the real-time balance within the microgrid in compliance with its technical-operational constraints. Lyapunov's theorem using sensitivity theory is adopted to solve this optimization.To test the performances of the proposed control methodology, several computer simulations corresponding to different operating scenarios have been conducted on the PrInCE Lab experimental microgrid built at the Polytechnic University of Bari.

A Co-evolutionary Multi-population Evolutionary Algorithm for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization problems (DMOPs) widely appear in various real-world applications and have attracted increasing attention worldwide. However, how to obtain both good population diversity and fast convergence speed to efficiently solve DMOPs are two challenging issues. Inspired by that the multiple populations for multiple objectives (MPMO) framework can provide algorithms with good population diversity and fast convergence speed, this paper proposes a new efficient algorithm called a co-evolutionary multi-population evolutionary algorithm (CMEA) based on the MPMO framework together with three novel strategies, which are helpful for solving DMOPs efficiently from two aspects. First, in the evolution control aspect, a convergence-based population evolution strategy is proposed to select the suitable population for executing the evolution in different generations, so as to accelerate the convergence speed of the algorithm. Second, in the dynamic control aspect, a multi-population-based dynamic detection strategy and a multi-population-based dynamic response strategy are proposed to help the algorithm maintain the population diversity, which are efficient for detecting and responding to the dynamic changes of environments. Integrating with the above strategies, the CMEA is proposed to solve the DMOP efficiently. The superiority of the proposed CMEA is validated in experiments on widely-used DMOP benchmark problems.

A novel preference-driven evolutionary algorithm for dynamic multi-objective problems

Most studies in dynamic multi-objective optimization have predominantly focused on rapidly and accurately tracking changes in the Pareto optimal front (POF) and Pareto optimal set (POS) when the environment undergoes changes. However, there are real-world scenarios where it is necessary to simultaneously solve changing objective functions and satisfy the preference of Decision Makers (DMs). In particular, the DMs may be only interested in a partial region of the POF, known as the region of interest (ROI), rather than requiring the entire POF. To meet the challenge of simultaneously predicting a changing POF and/or POS and dynamic ROI, this paper proposes a new dynamic multi-objective evolutionary algorithm (DMOEAs) based on the preference. The proposed algorithm consists of three key components: an evolutionary direction adjustment strategy based on changing reference points to accommodate shifts in preferences, an angle-based search strategy for tracking the varying ROI, and a hybrid prediction strategy that combines linear prediction models and population manifold estimation within the ROI to ensure convergence and distribution in scenarios where preferences remain unchanged. Experimental studies conducted on 30 widely used benchmark problems in which it outperforms contrasting algorithms on 71% of test suits. Empirical results demonstrate the significant advantages of the proposed algorithm over existing state-of-the-art DMOEAs.

A dynamic multi-objective optimization evolutionary algorithm with adaptive boosting

Dynamic multi-objective optimization problems (DMOPs) are prevalent in the real world, where the challenge in solving DMOPs is how to track the time-varying Pareto-optimal front (PF) and Pareto-optimal set (PS) quickly and accurately. However, balancing convergence and diversity is challenging as a single strategy can only address a particular type of DMOP. To solve this issue, a dynamic multi-objective optimization evolutionary algorithm with adaptive boosting (AB-DMOEA) is proposed in this paper. In the AB-DMOEA, an adaptive boosting response mechanism will increase the weights of high-performing strategies, including those based on prediction, memory, and diversity, which have been improved and integrated into the mechanism to tackle various problems. Additionally, the dominated solutions reinforcement strategy optimizes the population to ensure the effective operation of the above mechanism. In static optimization, the static optimization boosting mechanism selects the appropriate static multi-objective optimizer for the current problem. AB-DMOEA is compared with the other seven state-of-the-art DMOEAs on 35 benchmark DMOPs. The comprehensive experimental results demonstrate that the overall performance of the AB-DMOEA is superior or comparable to that of the compared algorithms. The proposed AB-DMOEA is also successfully applied to the smart greenhouses problem.

A dynamic multi-objective evolutionary algorithm based on Mahalanobis distance and intra-cluster individual correlation rectification

Responding quickly and accurately to environmental changes is a challenge in addressing dynamic multi-objective optimization problems (DMOPs). Although many dynamic multi-objective evolutionary algorithms (DMOEAs) have demonstrated impressive performance, there is still room for improvement in accurately predicting population behavior. To address this limitation, this paper proposes a prediction strategy based on Mahalanobis distance and intra-cluster individual correlation rectification (MCIR) to deal with DMOPs. First, a manifold clustering method is used to partition the Pareto set of the population into subpopulations, in which individuals with similar movement trends are grouped into clusters. Second, the Mahalanobis distance is introduced to systematically measure the relationships between clusters in adjacent environments. Time series models are established for each cluster center to predict their positions in the neighboring environment. On this basis, the movement characteristics of individuals within clusters are further rectified by calculating the correlation between intra-cluster individuals and the cluster center, facilitating more accurate tracking of the changing Pareto set/Pareto front. Finally, Gaussian noise is introduced to ensure the diversity of new individuals. The effectiveness of the MCIR algorithm is demonstrated by comparing it with four DMOEAs using 18 test instances. Experimental results confirm that MCIR holds great promise in addressing DMOPs.